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1
Content available Exact solution of the harmonic problem for a rectangular plate in flat deformation by the method of initial functions
Olodo E. T., Adanhounme V., Hounkonnou M. N.
International Journal of Applied Mechanics and Engineering
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2017
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Vol. 22, no. 2
349--361
EN
A wide range of applications is based nowadays on analytical developments which allow a precise and effective approach and short time of computations compared with the time required for numerical methods; in this way these developments are suitable for calculations in real time. This work proposes an approach for solving a two-dimensional harmonic problem of a rectangular plate under local surface loading using Vlasov’s symbolic method of initial functions and a general solution of the harmonic equation for a rectangle. Substituting the harmonic functions in symbolic form for the corresponding solutions allows us to give the exact solution of the problem in trigonometric form.
2
Regularity theorems for harmonic functions
Ganenkova E. G., Starkov V. V.
Journal of Applied Analysis
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2015
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Vol. 21, nr 1
25--36
EN
The regularity theorem is a result stating that functions which have extremal growth or decrease in the given class display a regular behaviour. Such theorems for linearly invariant families of analytic functions are well known. We prove regularity theorems for some classes of harmonic functions. Many presented statements are new even in the analytic case.
3
On Janowski harmonic functions
Dziok J.
Journal of Applied Analysis
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2015
|
Vol. 21, nr 2
99--107
EN
In this paper we define classes of harmonic functions related to the Janowski functions and we give some necessary and sufficient conditions for these classes. Some topological properties and extreme points of the classes are also considered. By using extreme points theory we obtain coefficients estimates, distortion theorems, integral mean inequalities for the classes of functions.
4
Zastosowanie funkcji harmonicznych do planowania ruchu i sterowania robotem dwukołowym
Szulczyński P., Pazderski D., Kozłowski K.
Prace Naukowe Politechniki Warszawskiej. Elektronika
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2010
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z. 175, t. 2
505-514
PL
Praca podejmuje problematykę planowania ruchu i sterowania robota mobilnego w środowisku dwuwymiarowym z eliptyczną przeszkodą statyczną w oparciu o metodę przepływu płynu. Opisano w niej algorytm projektowania strumienia dla przeszkody eliptycznej w przypadku celu statycznego i dynamicznego (trajektorii). Rozważania teoretyczne poparto wynikami symulacji numerycznych i wynikami badań eksperymentalnych, w których wykorzystano robota dwukołowego i metodę linearyzacji modelu kinematyki.
EN
The paper presents planning motion problem and control of mobile robot in two-dimensional environment with elliptical static obstacle based on hydrodynamics description. The design algorithm of the flow with respect to elliptical obstacle for static and dynamic goal is discussed. Theoretical considerations are supported by numerical simulations as well as experimental results using two-wheeled mobile robot and linearization technique.
5
Content available remote On polynomially bounded harmonic functions on the Zd lattice
Nayar P.
Bulletin of the Polish Academy of Sciences. Mathematics
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2009
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Vol. 57, no 3-4
231-242
EN
We prove that if ƒ : Zd → R is harmonic and there exists a polynomial W : Zd → R such that ƒ + W is nonnegative, then ƒ is a polynomial.
6
Content available remote On weighted harmonic Bergman spaces
Petrosyan A.
Demonstratio Mathematica
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2008
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Vol. 41, nr 1
73-83
EN
This paper is devoted to the investigation of the weighted Bergman harmonic spaces bp/alpha(B] in the unit ball in Rn. The reproducing kernel Ralpha for the ball is constructed and the integral representation for functions in bp/alpha(B) by means of this kernel is obtained. Besides an linear mapping between the bp/alpha(B) spaces and the ordinary L2-space on the unit sphere, which has an explicit form of integral operator along with its inversion, is established.
7
Content available remote On some coefficient conditions for complex harmonic mappings with a pole at the infinity
Sibelska A.
Demonstratio Mathematica
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2006
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Vol. 39, nr 2
335-346
EN
In 1984 J. Clunie and T. Sheil-Small initiated studies of complex functions harmonic in the unit disc. In 1987 W. Hergartner and G. Schober considered mappings of this type, defined in the domain U = {z is an element of C : \z\ > 1}. Several mathematicians examine classes of complex harmonic functions with some coefficient conditions, defined in the unit disc (e.g. [2], [5], [10], [1] [9]) or in U (e.g. [8], [7]). We investigate the classes of mappings harmonic in U with coefficient conditions more general than the considered in paper [8].
8
Content available remote On some generalization of coefficient conditions for complex harmonic mappings
Adamczyk G., Łazińska A.
Demonstratio Mathematica
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2004
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Vol. 37, nr 2
317--326
EN
Let h = u + iv, where u, v are real harmonic functions in the unit disc A. Such functions are called complex mappings harmonic in A. The function h may be written in the form h = f + g, where f,g are functions holomorphic in the unit disc, of course. Studies of complex harmonic functions were initiated in 1984 by J. Clunie and T. Sheil-Small ([2]) and were continued by many others mathematicians. We can find some papers on functions harmonic in A, satisfying certain coefficient conditions, e.g. [1], [4], [6], [7], [8]. We investigate some more general problem, i. e. a coefficient inequality with any fixed sequence of real positive numbers.
9
Second order differential subordinations and certain subordination relations
Kowalczyk Joanna
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2002
|
z. 26 [199]
97-106
EN
In the present paper the second order differential subordination (1 - alpha)f(z/z + alphaf'{z) + betazf(z) [...] 1 + Mz \z is an element of U) is investigated. The best dominant of subordination (1) is founded. Connections between subordination (1) and subordination of f(z)/z, f'{z) are given. Further the convexity of the function / satisfying the subordination (1) for special choice of parameters a, alpha, beta and M are derived.
10
Quasihomographies of the real line
Szynal Anetta
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2002
|
z. 26 [199]
155-164
EN
In this paper we present some properties of normalized (fixed in points x1, x2, infinity k-quasihomographies of the real line.
11
On complex mappings harmonic in the unit disc with some coefficient conditions
Łazińska Anna
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2002
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z. 26 [199]
107-116
EN
Let h = u + w, where u,v are real harmonic functions in the unit disc delta. Such functions are called complex mappings harmonic in delta. The function h may be written in the form h = f + g, where f, g are functions holomorphic in the unit disc, of course. Studies of complex harmonic functions were initiated in 1984 by J. Clunie and T. Sheil-Small ([CS-S]) and were continued by many others mathematicians. We can find some papers on functions harmonic in delta, satisfying certain coefficient conditions, e.g. [AZ], [S], [G]. We investigate some more general problems, which appeared during the seminar conducted by Professor Z. Jakubowski.
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